Physics by Lamhi: Not Your Boring Physics

CLASS 12 · CHAPTER 9 · OPTICS

QUICK REVISION

Ray Optics and Optical Instruments

Every key result from this chapter, boxed and ready for a last look before the exam. No derivations here, just what to recall and when to use it — for the full explanation, see the detailed notes.

1. Mirror Formula

Mirror formula
1v+1u=1f,m=−vu\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}, \qquad m=-\dfrac{v}{u}

Convex mirror: always virtual, erect, diminished, whatever the object distance.

2. Snell's Law

Snell's law
n1sin⁡θ1=n2sin⁡θ2n_1\sin\theta_1 = n_2\sin\theta_2

Denser → rarer: bends away from normal. Rarer → denser: bends toward normal.

3. Total Internal Reflection & Critical Angle — the exam trap

Critical angle
sin⁡θc=n2n1(n1>n2)\sin\theta_c = \dfrac{n_2}{n_1}\quad(n_1 > n_2)
  1. θ₁ < θc: refracted ray exists, bending away from the normal as usual.
  2. θ₁ = θc: refracted ray still exists, grazing exactly along the surface (θ₂ = 90°).
  3. θ₁ ≥ θc (even by a fraction of a degree): no refracted ray can exist at all — Snell’s law has no real solution. 100% total internal reflection, instantly, not a gradual fade.

Basis of optical fibres (light bounces the length of the fibre via repeated TIR) and why diamonds sparkle (high n → small θc).

4. Thin-Lens Formula

Thin-lens formula
1v−1u=1f\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}

Convex lens: f > 0 (converging). Concave lens: f < 0 (diverging).

5. Power of a Lens & Combinations

Power
P=1f (m) (dioptres),Pcombo=P1+P2+⋯P = \dfrac{1}{f\,(\text{m})}\ \text{(dioptres)}, \qquad P_{combo}=P_1+P_2+\cdots

6. Optical Instruments

  1. Simple microscope (image at near point D): m=1+D/fm=1+D/f; (image at infinity): m=D/fm=D/f.
  2. Astronomical telescope, normal adjustment: m=fo/fem=f_o/f_e — long objective, short eyepiece maximises magnification.

Full derivations and worked examples: detailed notes →